Method for simulating rough edge of mask in semiconductor photolithography process

Abstract

The application discloses a mask rough edge simulation method in a semiconductor photoetch process. By constructing a controllable space correlation noise model and accurately superimposing the controllable space correlation noise model on a mask physical boundary, combining with a signed distance field reconstruction, the simulation efficiency is significantly improved while the physical authenticity is maintained, so that large-scale statistical evaluation of extreme defects determining yield is realized, EDA support is provided for window optimization and reliability prediction of an advanced process, and thus the problems of high calculation cost of an existing high-fidelity simulation method and difficulty in efficiently statistically simulating extremely low-probability extreme defects are solved.

Description

Technical Field

[0001] This invention relates to the field of semiconductor manufacturing and electronic design automation simulation technology, and in particular to a method for simulating rough edges of a mask in semiconductor photolithography processes. Background Technology

[0002] As semiconductor process nodes advance to the nanoscale, the absolute accuracy of pattern dimensions has become the core factor determining chip performance and yield. LER (Line Edge Roughness), as a key metric for the fidelity of lithographic patterns, has evolved from a minor process noise into a systemic bottleneck restricting technological development.

[0003] Linear roughness (LER) originates from the inherent randomness of the photolithography process, mainly including photon shot noise, the discreteness of photoresist molecules, and statistical fluctuations in chemical reactions. In EUV (Extreme Ultraviolet) lithography, due to the sharp reduction in the number of effective photons, these random effects are significantly amplified, creating a fundamental contradiction between resolution, exposure dose, and line roughness.

[0004] More seriously, the geometric randomness caused by LER directly translates into fatal defects in transistor electrical characteristics. Research confirms that the edge roughness of the gate line is a significant intrinsic factor causing statistical fluctuations in key parameters such as threshold voltage and leakage current, and its impact in devices below 50 nanometers is comparable to that of random doping. This fluctuation is not symmetrically distributed, resulting in a much higher probability of catastrophic circuit failures such as local interconnect breakage or missing contact holes than predicted by traditional models. These extremely low-probability, extremely high-hazard defects are key to determining the yield of advanced process mass production. Therefore, high-fidelity and high-efficiency statistical simulation of the LER effect during the chip design stage has become a rigid requirement for evaluating process windows and predicting product reliability. Existing high-precision simulation methods, such as the fully discrete Monte Carlo method, can finely characterize microscopic physical processes, but due to the complexity of the models, the difficulty in obtaining parameters, and the extremely high computational cost, it is difficult to perform statistically significant large-scale sampling of extremely low-probability events that determine yield, resulting in bottlenecks in practical engineering applications. Although such methods are rich in physical detail, they have two fundamental limitations: first, the computational cost is extremely high. To achieve a certain level of statistical accuracy, the required sample size N and error... satisfy The relationship is that pursuing higher precision leads to a quadratic increase in computational load. Simulating extremely low-probability defects that determine chip yield requires massive sampling, which is often computationally infeasible. Second, the results have random variance. Different simulations will yield fluctuating results, lacking strict repeatability, which is not conducive to deterministic process optimization.

[0005] Therefore, the industry urgently needs a new simulation method that can achieve a breakthrough balance between physical fidelity and computational feasibility. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for simulating rough edges of masks in semiconductor lithography processes. By constructing a controllable spatially correlated noise model and accurately superimposing it onto the physical boundary of the mask, combined with symbolic distance field reconstruction, the simulation efficiency is significantly improved while maintaining physical realism. This enables large-scale statistical evaluation of extreme defects that determine yield, providing EDA (Electronic Design Automation) support for window optimization and reliability prediction in advanced processes.

[0007] This invention provides the following solutions:

[0008] This invention provides a method for simulating rough edges of a mask in semiconductor photolithography, the method comprising:

[0009] S1. Obtain the initial mask data of the target lithographic pattern and set the noise parameters;

[0010] S2, Generate a noise sequence;

[0011] S3. Extract and sort the mask boundary coordinates from the initial mask data to obtain the boundary point set;

[0012] S4. Use the noise sequence to perturb the physical coordinates of each point in the boundary point set to obtain the perturbed point set;

[0013] S5. Based on the perturbed point set, reconstruct the symbolic distance value, extract the zero isosurface, and obtain the lithographic pattern with controllable edge roughness.

[0014] Furthermore, the noise parameters mentioned in step S1 include the root mean square noise amplitude A, the correlation length ξ, and the attenuation index α.

[0015] Furthermore, different values ​​of α correspond to Gaussian noise and exponential noise, respectively.

[0016] Furthermore, step S2 involves performing a Fourier transform on the uniform white noise sequence and the autocorrelation function to obtain a noise sequence, where the i-th element is n. i .

[0017] Furthermore, step S3 includes the following processes:

[0018] S3.1 Calculate the symbolic distance field (SDF) of the initial mask data;

[0019] S3.2 Extract the zero contour lines of the target mask pattern from the symbolic distance field SDF, and obtain a set of discrete physical coordinate points after removing duplicate points;

[0020] S3.3. Sort the physical coordinate points in counterclockwise order to form an ordered and closed boundary. The sorted physical coordinate points form the boundary point set P0, where x i and y i , , and , respectively, are the horizontal and vertical physical coordinates of the i-th boundary point in the boundary point set.

[0021] Furthermore, step S4 includes the following process: taking each element in the noise sequence as a perturbation displacement, and superimposing it onto the physical coordinates of each boundary point in the boundary point set P0 in the normal direction to obtain the perturbed point set P1, where the x and y coordinates of the i-th point are x and x, respectively. i +n i ·n_x i and y i +n i ·n_y i , (n_x i ,n_y i ) is the unit normal vector of the i-th point in the boundary point set P0.

[0022] Furthermore, the reconstructing of the symbolic distance value in step S5 includes the following process: calculating the minimum Euclidean distance from each grid point in the simulation region to all points in the perturbed point set P1, and using geometric methods to determine the internal and external relationships of the grid points relative to the closed boundary formed by the perturbed point set P1, thereby assigning a signed distance value to form a new symbolic distance field SDF. new .

[0023] The beneficial effects of this invention based on its technical solution are as follows:

[0024] (1) The present invention provides a method for simulating rough edges of a mask in semiconductor lithography process. By constructing a controllable spatial correlation noise model and accurately superimposing it onto the physical boundary of the mask, combined with the reconstruction of the symbolic distance field, the simulation efficiency is significantly improved while maintaining physical authenticity. This enables large-scale statistical evaluation of extreme defects that determine yield, and provides EDA support for window optimization and reliability prediction of advanced processes. This solves the problems of high computational cost and difficulty in efficiently simulating extremely low probability extreme defects in existing high-fidelity simulation methods.

[0025] (2) The method for simulating mask roughness edges in semiconductor lithography provided by this invention abandons the traditional approach of directly sampling from microscopic physical processes. Instead, it creatively proposes a "geometric-statistical" equivalent model based on controllable spatially correlated noise, directly injecting random perturbations with clearly defined statistical characteristics (amplitude, correlation length) into the geometric level of the line edges. This method is equivalent to the physical model in terms of the statistical characteristics of the results, but reduces the computational complexity from the high cost of Monte Carlo methods, where the computational cost increases quadratically with the increase in accuracy requirements, to the fixed cost of one deterministic geometric processing and one distance field reconstruction. More importantly, for the same noise parameter seed, this invention can always generate a completely deterministic and repeatable roughness pattern, greatly improving the reliability and engineering practicality of the simulation process. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a flowchart illustrating a method for simulating rough edges of a mask in a semiconductor photolithography process, as provided by the present invention.

[0028] Figure 2 This is a schematic diagram of two types of noise sequences.

[0029] Figure 3 This is a schematic diagram for boundary extraction.

[0030] Figure 4 Comparison of edge roughness simulation results under different parameters. Detailed Implementation

[0031] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the protection scope of the embodiments of the present invention.

[0032] This embodiment provides a method for simulating rough edges of a mask in semiconductor photolithography processes, referring to... Figure 1 The method includes:

[0033] S1. Obtain the initial mask data of the target lithographic pattern and set the noise parameters, including the root mean square noise amplitude A, the correlation length ξ, and the attenuation exponent α. α=1 corresponds to Gaussian noise, and α=0.5 corresponds to exponential noise.

[0034] Figure 2 The image shows a comparison of two noise sequences with A=2 and ξ=10, where (1) and (2) are Gaussian and exponential noise sequences, respectively. It can be seen that under the same conditions, the Gaussian noise sequence is smoother.

[0035] S2. By performing a Fourier transform on the uniform white noise sequence and the autocorrelation function, a noise sequence is obtained, where the i-th element is n. i In this embodiment, the white noise generation interval is [-1, 1], and the autocorrelation function is:

[0036] .

[0037] S3. Extract and sort the mask boundary coordinates from the initial mask data to obtain the boundary point set, including the following process:

[0038] S3.1 Calculate the symbolic distance field (SDF) of the initial mask data;

[0039] S3.2. Use the Marching Square algorithm to extract the zero contour lines of the target mask pattern from the symbolic distance field SDF. After removing duplicate points, a set of discrete physical coordinate points that can accurately characterize the boundary of the pattern is obtained.

[0040] S3.3. The physical coordinate points are sorted counter-clockwise using an iterative nearest neighbor search method, forming an ordered and closed boundary. This correctly handles convex and concave boundaries, ensuring the topological correctness of subsequent steps. The sorted physical coordinate points form a boundary point set P0, where x... i and y i , , and , respectively, are the horizontal and vertical physical coordinates of the i-th boundary point in the boundary point set.

[0041] like Figure 3 As shown, “d ij " represents the SDF value of grid point (i,j), the red line is the zero contour line of the mask, and the black dot is the extracted boundary physical coordinate (x,j). i ,y i The blue arrow represents the calculated unit normal (n_x). i ,n_y i ).

[0042] S4. Treat each element in the noise sequence as a perturbation displacement and superimpose it onto the physical coordinates of each boundary point in the boundary point set P0 along the normal direction to obtain the perturbed point set P1, where the x and y coordinates of the i-th point are x and y respectively. i +n i ·n_x i and y i +n i ·n_y i , (n_x i ,n_y i ) is the unit normal vector of the i-th point in the boundary point set P0.

[0043] This step is performed in a continuous physical space, ensuring the geometric directness and physical rationality of the disturbance.

[0044] S5. Reconstructing Symbolic Distance Values ​​Based on the Perturbed Point Set: Calculate the minimum Euclidean distance from each grid point in the simulation region to all points in the perturbed point set P1, and use geometric methods (such as ray casting) to determine the internal / external relationship of the grid points relative to the closed boundary formed by the perturbed point set P1. Based on this, assign a signed distance value to each grid point, forming a new symbolic distance field (SDF). new Finally, from the new symbolic distance field SDF new Extract the zero isosurface to obtain a photolithographic pattern with controllable edge roughness.

[0045] Figure 4 The simulation results under different parameters are shown in the comparison chart. Among them, (1) the parameters are A=1.00nm, ξ=5.0nm, α=0.5; (2) the parameters are A=1.00nm, ξ=5.0nm, α=1.0; (3) the parameters are A=1.00nm, ξ=10.0nm, α=0.5; (4) the parameters are A=1.00nm, ξ=10.0nm, α=1; (5) the parameters are A=1.00nm, ξ=10.0nm, α=0.5; (6) the parameters are A=1.00nm, ξ=10.0nm, α=1.0. It can be seen that the larger A is, the larger the amplitude of the noise; the larger ξ is, the lower the cutoff frequency of the noise, the smaller the high-frequency wave component, and the smoother the edge of the mask; conversely, the larger ξ is, the smaller the correlation length, the higher the cutoff frequency of the noise, the larger the high-frequency wave component, and the rougher the edge of the mask. All other things being equal, exponential noise is coarser than Gaussian noise.

[0046] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0047] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0048] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for simulating rough edges of a mask in a semiconductor photolithography process, characterized in that, The method includes: S1. Obtain the initial mask data of the target lithographic pattern and set the noise parameters; S2, Generate a noise sequence; S3. Extract and sort the mask boundary coordinates from the initial mask data to obtain the boundary point set; S4. Use the noise sequence to perturb the physical coordinates of each point in the boundary point set to obtain the perturbed point set; S5. Based on the perturbed point set, reconstruct the symbolic distance value, extract the zero isosurface, and obtain the lithographic pattern with controllable edge roughness.

2. The method for simulating rough edges of a mask in semiconductor photolithography according to claim 1, characterized in that: The noise parameters mentioned in step S1 include the root mean square noise amplitude A, the correlation length ξ, and the attenuation index α.

3. The method for simulating rough edges of a mask in semiconductor photolithography according to claim 2, characterized in that: Different values ​​of α correspond to Gaussian noise and exponential noise, respectively.

4. The method for simulating rough edges of a mask in semiconductor photolithography according to claim 1, characterized in that: Step S2 involves performing a Fourier transform on the uniform white noise sequence and the autocorrelation function to obtain a noise sequence, where the i-th element is n. i .

5. The method for simulating rough edges of a mask in semiconductor photolithography according to claim 1, characterized in that: Step S3 includes the following processes: S3.1 Calculate the symbolic distance field (SDF) of the initial mask data; S3.2 Extract the zero contour lines of the target mask pattern from the symbolic distance field SDF, and obtain a set of discrete physical coordinate points after removing duplicate points; S3.

3. Sort the physical coordinate points in counterclockwise order to form an ordered and closed boundary. The sorted physical coordinate points form the boundary point set P0, where x i and y i , , and , respectively, are the horizontal and vertical physical coordinates of the i-th boundary point in the boundary point set.

6. The method for simulating rough edges of a mask in semiconductor photolithography according to claim 4 or 5, characterized in that: Step S4 includes the following process: Each element in the noise sequence is used as a perturbation displacement, and superimposed onto the physical coordinates of each boundary point in the boundary point set P0 in the normal direction to obtain the perturbed point set P1, where the x and y coordinates of the i-th point are x and x, respectively. i +n i ·n_x i and y i +n i ·n_y i , (n_x i ,n_y i ) is the unit normal vector of the i-th point in the boundary point set P0.

7. The method for simulating rough edges of a mask in semiconductor photolithography according to claim 1, characterized in that: Step S5 involves reconstructing the symbolic distance value, which includes the following process: calculating the minimum Euclidean distance from each grid point in the simulation region to all points in the perturbed point set P1, and using geometric methods to determine the internal and external relationships of the grid points relative to the closed boundary formed by the perturbed point set P1. Based on this, a signed distance value is assigned, forming a new symbolic distance field SDF. new .

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